Hello, Cataclysm!
If you made a sketch, the answer is obvious . . .
Find the equation of the focal chord that cuts the curve $\displaystyle x^2\:=\:8y$ at (4, 2) From the equation, $\displaystyle x^2 \:=\:8y$, we know all this:
. . The parabola opens upward.
. . Its vertex is at the origin.
. . The focus is at (0, 2).
Code:

*  *

* F(0,2) *
(4,2)*    o    *
*  *
*  *
*

The focal chord that contains (4, 2) is the horizonal line: .$\displaystyle y \:=\:2$